Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth.
$c = \square$ miles

Explanation:

Step1: Identify the formula

For a right triangle, we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. Here, \(a = 4\) mi, \(b = 5\) mi.

Step2: Substitute values

Substitute \(a = 4\) and \(b = 5\) into the formula: \(4^2 + 5^2 = c^2\). Calculate \(4^2 = 16\) and \(5^2 = 25\), so \(16 + 25 = c^2\).

Step3: Simplify the equation

\(16 + 25 = 41\), so \(c^2 = 41\).

Step4: Solve for \(c\)

Take the square root of both sides: \(c = \sqrt{41}\). Calculate \(\sqrt{41} \approx 6.4\) (rounded to the nearest tenth).

Answer:

\(6.4\)